Accelerometer simulation.
Classes:
| Name | Description |
|---|---|
AccelerometerSpecification |
Accelerometer specification. |
AccelerometerData |
Accelerometer output data. |
Accelerometer |
Simulate accelerometer sensors. |
AccelerometerSpecification(axes: int = NUM_CARTESIAN_AXES)
Bases: SensorSpecification
Accelerometer specification.
An accelerometer specification includes the parameters required to simulate accelerometer response to ideal inputs. These include input limits, noise coefficients, biases, scale factors, and internal sensor misalignments.
By default the specification returns a perfect sensor whose output will precisely match its sensed input.
Classes:
| Name | Description |
|---|---|
DataInterface |
An abstract base class for data interface parameters. |
InputLimits |
Sensor input limits. |
Noise |
Sensor noise terms. |
Bias |
Sensor bias terms. |
ScaleFactor |
Sensor scale factor terms. |
Misalignment |
Sensor misalignment. |
AccelerometerDataInterface |
Accelerometer data interface parameters. |
AccelerometerInputLimits |
Accelerometer input limits. |
AccelerometerNoise |
Accelerometer noise terms. |
AccelerometerBias |
Accelerometer bias terms. |
Attributes:
| Name | Type | Description |
|---|---|---|
axes |
int
|
Number of independent sensing axes of the sensor. |
manufacturer |
str
|
Manufacturer of the sensor. |
model |
str
|
Model number/identifier of the sensor. |
version |
str
|
Version number/identifier of the sensor. |
data_interface |
DataInterface
|
Sensor data interface specifications. |
scale_factor |
ScaleFactor
|
Sensor scale factor specification. |
misalignment |
Misalignment
|
A sensor misalignment specification. |
input_limits |
AccelerometerInputLimits
|
An accelerometer input limits specification. |
noise |
AccelerometerNoise
|
An accelerometer noise specification. |
bias |
AccelerometerBias
|
An accelerometer bias specification. |
deletable
property
writable
¶
data_interface: DataInterface
Sensor data interface specifications.
property
¶
input_limits: AccelerometerInputLimits
An accelerometer input limits specification.
DataInterface(axes: int)
Bases: ABC
An abstract base class for data interface parameters.
The data interface of the sensor. The sensor interface includes the data frequency, which is the frequency at which the sensor transmits new data, and the data type, which is one of rate or delta.
Derived classes should set appropriate defaults and handle units in the setter methods.
Attributes:
| Name | Type | Description |
|---|---|---|
sample_rate |
Parameter
|
The frequency at which new data is output from the sensor. |
delta_sample_rate |
Parameter
|
The frequency at which delta type data is output from the sensor. |
quantization |
Parameter | None
|
Data interface rate output quantization. |
delta_quantization |
Parameter | None
|
Data interface delta output quantization. |
delta_stride |
int
|
Integer number of rate outputs per delta output. |
property
writable
¶
sample_rate: Parameter
The frequency at which new data is output from the sensor.
Units must be "Hz".
Default value = Parameter(100, "Hz").
property
writable
¶
delta_sample_rate: Parameter
The frequency at which delta type data is output from the sensor.
Units must be "Hz" and must be a integer divisor of sample_rate.
Default value = Parameter(0, "Hz") meaning no delta outputs.
abstractmethod
property
writable
¶
quantization: Parameter | None
Data interface rate output quantization.
Outputs will be quantized at simulated digital levels. Use this when the parameters of the analog to digital conversion are known. If the sensor to simulate has been characterized experimentally, e.g. by the Allan deviation method, use Noise.quantization instead. Do not use both.
abstractmethod
property
writable
¶
delta_quantization: Parameter | None
Data interface delta output quantization.
Delta (integrated) outputs will be quantized at simulated digital levels. Use this when the parameters of the analog to digital conversion are known. If the sensor to simulate has been characterized experimentally, e.g. by the Allan deviation method, use Noise.quantization instead. Do not use both.
InputLimits(axes: int)
Bases: ABC
Sensor input limits.
The extreme values of the input (negative and positive) within which performance is of the specified accuracy. Simulated outputs outside of this range are truncated to these limits.
Derived classes should set appropriate defaults and handle units in the setter methods.
Attributes:
| Name | Type | Description |
|---|---|---|
minimum |
Parameter
|
Minimum negative input. |
maximum |
Parameter
|
Maximum positive input. |
Noise(axes: int)
Bases: ABC
Sensor noise terms.
Common inertial sensor noise terms describing quantization, random walk, bias instability, rate random walk, and rate ramp. See Reference [20] and Standard [05] & Standard [06] for details.
Each of these noise terms can be determined experimentally from Allan variance/deviation plots or from data sheets and direct knowledge of the sensor. Not all terms will be applicable to all sensors.
Derived classes should set appropriate defaults and handle units in the setter methods.
Attributes:
| Name | Type | Description |
|---|---|---|
quantization |
Parameter
|
Quantization noise. |
random_walk |
Parameter
|
Random walk noise. |
bias_instability |
Parameter
|
Bias instability noise. |
rate_random_walk |
Parameter
|
Rate random walk noise. |
rate_ramp |
Parameter
|
Rate ramp noise. |
abstractmethod
property
writable
¶
quantization: Parameter
Quantization noise.
Uniformly distributed random noise arising from digital quantization of the input. Use this parameter when the sensor to simulate has been characterized experimentally, e.g. by the Allan deviation method. If the parameters of the analog to digital converter are known explicitly, use ScaleFactor.quantization instead. Do not use both.
abstractmethod
property
writable
¶
random_walk: Parameter
Random walk noise.
Random white noise in the signal that when integrated results in error buildup. Also known equivalently as noise density.
abstractmethod
property
writable
¶
bias_instability: Parameter
Bias instability noise.
The random variation in bias as computed over specified finite sampling time and averaging time intervals. Also known equivalently as bias in-run stability and flicker noise.
Bias(axes: int)
Bases: ABC
Sensor bias terms.
Bias is the non-zero output of a sensor at rest, or equivalently, the output that has no correlation with the input. It is comprised of a fixed component (that can be calibrated), a random component (that may vary from turn-on to turn-on or with changing conditions), and a temperature dependent component.
Derived classes should set appropriate defaults and handle units in the setter methods.
Attributes:
| Name | Type | Description |
|---|---|---|
fixed |
Parameter
|
Fixed bias. |
repeatability |
Parameter
|
Random bias. |
temperature |
Parameter
|
Temperature bias. |
abstractmethod
property
writable
¶
fixed: Parameter
Fixed bias.
A fixed bias that is constant across all conditions. For many sensors, this may be removed by factory calibration in which case this parameter can represent any known residual error in that calibration.
abstractmethod
property
writable
¶
repeatability: Parameter
Random bias.
The standard deviation of a random bias component that varies with each turn-on of the sensor and/or varies across external conditions. This parameter may represent unknown residuals from the factory calibration of a fixed bias.
ScaleFactor(axes: int)
Sensor scale factor terms.
Scale factor is the ratio of change in output to change in input at the analog sensing elements.
A perfect sensor has a linear analog response with a scale of 1.0. Imperfect sensors may have a non-unit scale.
Attributes:
| Name | Type | Description |
|---|---|---|
fixed |
Parameter
|
Fixed scale factor error. |
repeatability |
Parameter
|
Random scale factor error. |
property
writable
¶
fixed: Parameter
Fixed scale factor error.
A fixed offset from the ideal unit scale factor (1.0) that is
constant across all conditions. For many sensors, this may be
removed by factory calibration in which case this parameter can
represent any known residual error in that calibration. Units are
ratios of similar quantities so must be one of: "dimensionless",
"%", or "ppm".
Default value = Parameter([0.0,0.0,0.0], "dimensionless").
property
writable
¶
repeatability: Parameter
Random scale factor error.
The standard deviation of a random scale factor error that varies
with each turn-on of the sensor and/or varies across external
conditions. This parameter may represent unknown residuals from the
factory calibration of fixed scale factor. Units are ratios of
similar quantities so must be one of: "dimensionless", "%", or
"ppm".
Default value = Parameter([0.0,0.0,0.0], "dimensionless").
Misalignment(axes: int)
Sensor misalignment.
Misalignment is the offset between the ideal orthogonal input reference axes (IRA) and the actual sensitive input axis (IA) of the sensor. It is comprised of a fixed component (that can be calibrated) and a random component (that may vary from turn-on to turn-on or with changing conditions).
See Standard [05] and Standard [06] for details.
Attributes:
| Name | Type | Description |
|---|---|---|
fixed |
Parameter
|
Fixed sensor alignment. |
repeatability |
Parameter
|
Random sensor misalignment. |
property
writable
¶
fixed: Parameter
Fixed sensor alignment.
Coordinate transform matrix converting 3-dimensional input reference
axes (IRA) to N-dimensional input axes (IA). IRA are also known as
platform axes and the IA are also known as accelerometer, gyro, or
sensor axes. The resulting matrix is Nx3 where N is the number of
measurement axes of the device. For an ideal sensor this will
typically be an identity matrix. For real sensors, the deviation
from identity represents the misalignment. This fixed misalignment
may be removed by factory calibration in which case this parameter
can represent any residual error in that calibration. Units must be
"dimensionless". For sensors with <= 3 axes, the default value is a
one-to-one map of input axes to the available output axes. For
example, in a default 2-axis sensor input x-y axes map to output x-y
axes: Parameter([[1,0,0],[0,1,0]],"dimensionless"). The input
z-axis is not sensed. For sensors with > 3 axes, inputs are
duplicated in sequence to fill the output. For example, by default
a 4-axis sensor will duplicate the x input:
Parameter([[1,0,0],[0,1,0],[0,0,1],[1,0,0]],"dimensionless"). This
is typically not how redundant sensor designs are aligned so users
should take care to supply the correct input in these cases. An
example of a single axis sensor with a fixed, known misalignment is:
Parameter([0.999,0.02,-0.04],"dimensionless"). This maps IRA
inputs to a single output with a known misalignment.
Default value = Parameter(np.eye(3), "rad").
property
writable
¶
repeatability: Parameter
Random sensor misalignment.
Standard deviation of a (small) random angle offset applied to the
each input axis (IA). Each axis is independently rotated, meaning
that the result is non-orthogonal. The random offset is applied as
a rotation vector with components sampled independently around each
of the 3 input reference axes (IRA). For example, a single axis
sensor has a default fixed axis of:
Parameter([1,0,0],"dimensionless"). That axis will be rotated
according to:
rotation_vector = repeatability * rng.std_normal(shape=(3,1))
axis = Rotation.from_rotation_vector(rotation_vector) @ [1,0,0]
Parameter([0.999,0.02,-0.04],"dimensionless"). This process is
repeated for each axis. This parameter may represent an unknown
residual from the factory calibration or an offset that varies with
changing conditions like packaging stress and shock. Units must be
one of: "rad" or "deg".
Default value = Parameter([0.0,0.0,0.0], "rad") per axis.
AccelerometerDataInterface(axes: int)
Bases: DataInterface
Accelerometer data interface parameters.
The data interface includes the data rate, which is the frequency at which the sensor transmits new data, the data type, and any digital quantization in the data.
Attributes:
| Name | Type | Description |
|---|---|---|
sample_rate |
Parameter
|
The frequency at which new data is output from the sensor. |
delta_sample_rate |
Parameter
|
The frequency at which delta type data is output from the sensor. |
delta_stride |
int
|
Integer number of rate outputs per delta output. |
quantization |
Parameter | None
|
Data interface rate output quantization. |
delta_quantization |
Parameter | None
|
Data interface delta output quantization. |
property
writable
¶
sample_rate: Parameter
The frequency at which new data is output from the sensor.
Units must be "Hz".
Default value = Parameter(100, "Hz").
property
writable
¶
delta_sample_rate: Parameter
The frequency at which delta type data is output from the sensor.
Units must be "Hz" and must be a integer divisor of sample_rate.
Default value = Parameter(0, "Hz") meaning no delta outputs.
property
writable
¶
quantization: Parameter | None
Data interface rate output quantization.
Outputs will be quantized at simulated digital levels. Use this when
the parameters of the analog to digital conversion are known. If
the sensor to simulate has been characterized experimentally, e.g.
by the Allan deviation method, use AccelerometerNoise.quantization
instead. Do not use both. Units must be one of: "m/s/s/LSB",
"g/LSB", or "ft/s/s/LSB".
Default value = None.
property
writable
¶
delta_quantization: Parameter | None
Data interface delta output quantization.
Delta velocity outputs will be quantized at simulated digital
levels. Use this when the parameters of the analog to digital
conversion are known. If the sensor to simulate has been
characterized experimentally, e.g. by the Allan deviation method,
use AccelerometerNoise.quantization instead. Do not use both.
Delta velocity outputs will be integrated with un-quantized specific
force and angular rates before output. They are only available when
gyro data is also available, as in an IMU sensor. Units must be one
of: "m/s/LSB" or "ft/s/LSB".
Default value = None.
AccelerometerInputLimits(axes: int)
Bases: InputLimits
Accelerometer input limits.
The extreme values of the input (negative and positive) within which performance is of the specified accuracy. Simulated outputs outside of this range are truncated to the limits.
Attributes:
| Name | Type | Description |
|---|---|---|
minimum |
Parameter
|
Minimum negative input. |
maximum |
Parameter
|
Maximum positive input. |
AccelerometerNoise(axes: int)
Bases: Noise
Accelerometer noise terms.
Common accelerometer noise terms describing quantization, (velocity) random walk, bias instability, rate (acceleration) random walk, and rate (acceleration) ramp. See Reference [20] and Standard [06] for details. Note that "rate" is sometimes used specifically in the context of gyros (angular rate) but the term extends naturally to accelerometers (velocity rate = acceleration) as in Reference [20].
Each of these noise terms can be determined experimentally from Allan variance/deviation plots or from data sheets and direct knowledge of the sensor. Not all terms will be applicable to all sensors.
Attributes:
| Name | Type | Description |
|---|---|---|
quantization |
Parameter
|
Quantization noise. |
random_walk |
Parameter
|
Random walk noise. |
bias_instability |
Parameter
|
Bias instability noise. |
rate_random_walk |
Parameter
|
Rate random walk noise. |
rate_ramp |
Parameter
|
Rate ramp noise. |
property
writable
¶
quantization: Parameter
Quantization noise.
Uniformly distributed random noise arising from digital quantization
of the input. Use this parameter when the sensor to simulate has
been characterized experimentally, e.g. by the Allan deviation
method. If the parameters of the analog to digital converter are
known explicitly, use AccelerometerDataInterface.quantization
instead. Do not use both. Units must be one of: "m/s" or
"ft/s".
Default value = Parameter([0.0,0.0,0.0], "m/s").
property
writable
¶
random_walk: Parameter
Random walk noise.
Random white noise in the acceleration signal that when integrated
results in velocity error buildup (velocity random walk). Also
known equivalently as noise density. Units must be one of:
"m/s/sqrt(s)", "m/s/s/sqrt(Hz)", "m/s/sqrt(h)",
"g/sqrt(Hz)", "ft/s/sqrt(s)", "ft/s/s/sqrt(Hz)", or
"ft/s/sqrt(h)".
Default value = Parameter([0.0,0.0,0.0], "m/s/sqrt(s)").
property
writable
¶
bias_instability: Parameter
Bias instability noise.
The random variation in bias as computed over specified finite
sampling time and averaging time intervals. Also known equivalently
as bias stability and flicker noise. Units must be one of:
"m/s/s", "g", or "ft/s/s".
Default value = Parameter([0.0,0.0,0.0], "m/s/s").
property
writable
¶
rate_random_walk: Parameter
Rate random walk noise.
Random white noise in the acceleration derivative (jerk) that
results in acceleration error buildup (acceleration random walk).
Note that "rate" is sometimes used specifically in the context of
gyros (angular rate) but for commonality the term extends here to
accelerometers (velocity rate = acceleration) as in Reference
[20]. Units must be one of: "m/s/s/sqrt(s)",
"g/sqrt(h)", "ft/s/s/sqrt(s)".
Default value = Parameter([0.0,0.0,0.0], "m/s/s/sqrt(s)").
AccelerometerBias(axes: int)
Bases: Bias
Accelerometer bias terms.
Bias is the non-zero output of a sensor at rest, or equivalently, the output that has no correlation with the input. It is comprised of a fixed component (that can be calibrated), a random component (that may vary from turn-on to turn-on or with changing conditions), and a temperature dependent component.
Attributes:
| Name | Type | Description |
|---|---|---|
fixed |
Parameter
|
Fixed bias. |
repeatability |
Parameter
|
Random bias. |
temperature |
Parameter
|
Temperature bias. |
property
writable
¶
fixed: Parameter
Fixed bias.
A fixed bias that is constant across all conditions. For many
sensors, this may be removed by factory calibration in which case
this parameter can represent any known residual error in that
calibration. Units must be one of: "m/s/s", "g", or "ft/s/s".
Default value = Parameter([0.0,0.0,0.0], "m/s/s").
property
writable
¶
repeatability: Parameter
Random bias.
The standard deviation of a random bias component that varies with
each turn-on of the sensor and/or varies across external conditions.
This parameter may represent unknown residuals from the factory
calibration of a fixed bias. Units must be one of: "m/s/s",
"g", or "ft/s/s".
Default value = Parameter([0.0,0.0,0.0], "m/s/s").
property
writable
¶
temperature: Parameter
Temperature bias.
A linear coefficient relating change in sensor temperature to a
change in bias. Units must be one of: "m/s/s/C", "g/C",
"ft/s/s/C", "g/F", or "ft/s/s/F". Note: for change in
temperature (delta), the Celsius (C) and Kelvin (K) scales are
equivalent, so units per Kelvin are implicitly supported.
Default value = Parameter([0.0,0.0,0.0], "m/s/s/C").
dataclass
¶
AccelerometerData(
*,
specific_force: Measurement,
delta_velocity: Measurement | None = None,
)
Accelerometer output data.
An instance of this class is returned from the Accelerometer.simulate method. It contains the simulated specific force and delta velocity (optional) measurements.
Attributes:
| Name | Type | Description |
|---|---|---|
specific_force |
Measurement
|
|
delta_velocity |
Measurement | None
|
|
Accelerometer(
model: SensorModel | IMUModel,
specification: AccelerometerSpecification | IMUSpecification,
rng: Generator | int | None = None,
)
Accelerometer(
model: SensorModel | IMUModel,
specification: AccelerometerSpecification | IMUSpecification,
rng: Generator | int | None = None,
*,
mode: str = "real-time",
max_duration: float,
)
Accelerometer(
model: SensorModel | IMUModel,
specification: AccelerometerSpecification | IMUSpecification,
rng: Generator | int | None = None,
*,
mode: str = "batch",
max_duration: float | None = None,
)
Bases: Sensor
Simulate accelerometer sensors.
An accelerometer is "an inertial sensor that measures the component of translational acceleration minus the component of gravitational acceleration along its input axis(es)" [Standard 03].
Accelerometers requires a model which specifies which sources of error to simulate; a specification which includes the parameters necessary to model deterministic and random errors; and optionally a random number generator or seed to control determinism and repeatability of the simulation.
Two modes are supported: batch (default) and real-time. In batch
mode, the simulate() method should be called once with all inputs to
return all simulated measurement outputs. In real-time mode, the
simulate() method can be called repeatedly to incrementally simulate
measurements. In real-time mode, a max_duration input (specified in
seconds) should supply an upper bound on the expected simulation
duration. If the expected duration is unknown it is safe and efficient
to specify a value up to several hours.
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
model
|
SensorModel | IMUModel
|
Accelerometer or IMU model. |
required |
specification
|
AccelerometerSpecification | IMUSpecification
|
Accelerometer or IMU specification. |
required |
rng
|
Generator | int | None
|
Random number generator or seed. See numpy.random.default_rng. |
None
|
mode
|
str
|
One of |
'batch'
|
max_duration
|
float | None
|
The maximum simulation duration in seconds. If simulating in
|
None
|
Methods:
| Name | Description |
|---|---|
simulate |
Simulate accelerometer measurements from kinematic inputs. |
Attributes:
| Name | Type | Description |
|---|---|---|
state |
SimulationState
|
Simulation state. |
property
¶
state: SimulationState
Simulation state.
Return the simulation state. The state includes the sensor model; the sensor specification; the random number generator state at initialization; and the value of all internal sensor parameters required to replicate the simulated measurement outputs.
simulate(
*,
specific_force: Vector,
temperature: ArrayLike | None = None,
) -> AccelerometerData
simulate(
*,
acceleration: Vector,
global_pose: GlobalPose,
temperature: ArrayLike | None = None,
) -> AccelerometerData
simulate(
*,
global_pose: GlobalPose,
temperature: ArrayLike | None = None,
) -> AccelerometerData
simulate(
*,
specific_force: Vector | None = None,
acceleration: Vector | None = None,
global_pose: GlobalPose | None = None,
temperature: ArrayLike | None = None,
) -> AccelerometerData
Simulate accelerometer measurements from kinematic inputs.
All inputs are optional. Measurement outputs are calculated based on
the best available inputs. Insufficient inputs to calculate a valid
output will raise a ValueError.
Measurement output sample rate(s) will match the input sample rate. In
batch mode (default), if the simulate_sample_rate model option is
True, the output sample rate(s) will match the sample rate(s) in the
sensor specification. Linear interpolation of specific force is used
for the resampling.
All inputs are reduced to specific force internally and sources of error from the accelerometer specification are then applied to produce the measurement output(s).
The supported combination of inputs are:
specific_force: the input must be the specific force
(non-gravitational acceleration) acting on the accelerometer as measured
in accelerometer coordinates. This option can be used if no information
is known about the attitude and position of the accelerometer relative
to Earth (global pose) but it implies that the input must already
account for the effect of gravity.
acceleration + global_pose: the input must be the total acceleration
(including gravity) acting on the accelerometer as measured in
accelerometer coordinates. The effect of Earth's gravity (not measured
by the accelerometer) will be compensated based on the global_pose
data to produce specific force. If needed, the global_pose input will
be interpolated to match the times of the acceleration input. For
this reason, global_pose time stamps must match or span the entire
duration of the acceleration input.
global_pose: acceleration is numerically calculated as the first
forward difference of the global velocity (if available) or the second
forward difference of the global position. The effect of Earth's gravity
(not measured by the accelerometer) will be compensated to produce
specific force. At least two poses must be supplied. In real-time
mode, overlapping inputs should be supplied, e.g. pairwise poses (1-2,
2-3, 3-4, ...).
The temperature input is always optional. If included, it will be
used in combination with any temperature dependent specifications when
simulating measurement outputs.
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
specific_force
|
Vector | None
|
Specific force experienced by the accelerometer. |
None
|
acceleration
|
Vector | None
|
Total acceleration experienced by the accelerometer. |
None
|
global_pose
|
GlobalPose | None
|
Attitude and position of the accelerometer relative to Earth. |
None
|
temperature
|
ArrayLike | None
|
Array of temperatures corresponding to the primary input (degrees C). |
None
|
Returns:
| Name | Type | Description |
|---|---|---|
result |
AccelerometerData
|
AccelerometerResult instance. |